A note on advection-diffusion cholera model with bacterial hyperinfectivity (Q1979591)

In the recent paper by \textit{X. Wang} and \textit{F.-B. Wang} [J. Math. Anal. Appl. 480, No. 2, Article ID 123407, 29 p. (2019; Zbl 1423.92241)] a system of advection-diffusion equations was suggested to model the transmission of cholera. The authors complement these results proving two new theorems in the paper under review. Namely, Theorem 1.2 establishes local asymptotic stability and global attractivity of the cholera-free equilibrium \(E_{0}\) for the case when the basic reproduction number \(\mathcal{R}_{0}=1.\) For \(\mathcal{R}_{0}>1,\) Theorem 1.3 furnishes sufficient conditions for global asymptotic stability of the positive equilibrium \(E^{\ast}.\)